If a military veteran went to the hospital with an obvious wound, it’s natural to expect that treatment would commence without delay.

But not every war injury is immediately apparent or visible to the untrained eye.

With the wind-down of military operations in Iraq and Afghanistan, thousands of the returning troops are seeking care for mental-health issues stemming from their service experiences.

But the Veterans Affairs Department’s inspector general says many of those vets aren’t being seen as quickly as they should be -- and the VA’s flawed tracking system gives a false picture of the problem’s magnitude.

Even though the Veterans Health Administration reported in 2011 that 95 percent of veterans received a comprehensive mental exam within 14 days of requesting one (the time frame in agency policy), the actual number was 49 percent, the inspector general reported Monday. It took an average of 50 days to provide a full evaluation for the rest, the report said.

“VHA does not have a reliable and accurate method of determining whether they are providing patients timely access to mental health care services,” the inspector general said.

Part of the problem is with the way records are kept: Schedulers don’t always follow the rules, and the lag between referral by a primary care physician and the evaluation might not be reflected properly.

Part of the problem is a shortage of personnel, particularly psychiatrists. Officials knew the data-keeping was problematic; the inspector general pointed it out in reports in 2005 and 2007.

They also knew of the growing staffing needs and, in fact, increased personnel 46 percent from 2005 to 2010, the report said. But in an informal survey of VA mental-health professionals, requested by Congress, 71 percent of those responding said their centers didn’t have enough people to keep up. A veteran seeking treatment at the VA medical center in Salisbury, N.C., for instance, had to wait 86 days to see a psychiatrist, the IG said.

“Getting our veterans timely mental health care can quite frankly often be the difference between life and death,” said Sen. Patty Murray, a Washington state Democrat who heads the Senate Veterans’ Affairs Committee. “It’s the critical period, not unlike the ‘golden hour’ immediately after a traumatic physical injury.”

Indeed, the report cited studies in nonmilitary settings showing that delays in initially screening for mental-health needs tend to discourage patients from keeping appointments and following through with treatment.

Murray said the report “shows that the VA is failing many of those who have been brave enough to seek care. It is hard enough to get veterans into the VA system to receive mental-health care. Once a veteran takes the step to reach out for help, we need to knock down every potential barrier to care.”

Last week, Veterans Affairs Secretary Eric Shinseki said the department will add 1,600 mental-health clinicians, including nurses, psychiatrists, psychologists and social workers, plus 300 support workers. The Texas network of facilities will receive 140 new mental-health positions, a spokeswoman said, but it’s not certain how many will go to the Fort Worth Outpatient Clinic or the Dallas VA Medical Center.

Last year alone, the VA provided mental-health services to 1.3 million veterans, the agency said.

Of the 111,000 veterans served in Dallas, 25 percent receive mental-health care; of the 29,000 vets treated at the Fort Worth clinic, about 30 percent receive mental-health services. A spokeswoman said Tuesday that patients at the North Texas facilities get initial mental-health assessments and emergency services the day they seek them, though there might be a wait to start specific programs. The hospitals are working to improve their services and wait-time tracking, local officials said.

“History shows that the costs of war will continue to grow for a decade or more after the operational missions in Iraq and Afghanistan have ended,” Shinseki said.

It’s an obligation the American public has to those who’ve served, and it must be fulfilled as diligently as they served us.